ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of SmFe5 (Materials Project id mp-1566)

       169       59       75        0        0       -2  
        59      175       74        0        0       -2  
        75       74      239        0        0        1  
         0        0        0       67        0        0  
         0        0        0        0       68        0  
        -2       -2        1        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 111 GPaEV = 159.36 GPaGV = 63.2 GPaνV = 0.26073
ReussKR = 107.26 GPaER = 156.45 GPaGR = 62.238 GPaνR = 0.2569
HillKH = 109.13 GPaEH = 157.91 GPaGH = 62.719 GPaνH = 0.25884

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55.893 GPa 67 GPa 68 GPa 112.58 GPa 130.08 GPa 340.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 134.25 GPa 190.81 GPa 1.8549 TPa–1 3.882 TPa–1 55.934 GPa 68 GPa0.226840.34728Value
Anisotropy 1.421 2.0929 1.216 1.5309Anisotropy
Axis 0.8605
0.5095
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8984
0.4391
0.0000
0.0407
0.9992
-0.0000
0.0000
0.0000
1.0000
-0.5431
0.8397
0.0000
-0.0001
-0.0001
1.0000
Axis
-0.9992
0.0407
0.0000
-1.0000
0.0000
0.0000
0.0000
-0.0000
1.0000
-0.8764
-0.4816
-0.0001
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane